Machine learning has become the best approach to building systems that comprehend human language. However, current systems require a great deal of laboriously constructed human-annotated training data. Ideally, a computer would be able to acquire language like a child by being exposed to linguistic input in the context of a relevant but ambiguous perceptual environment. As a step in this direction, we have developed systems that learn to sportscast simulated robot soccer games and to follow navigation instructions in virtual environments by simply observing sample human linguistic behavior. This work builds on our earlier work on supervised learning of semantic parsers that map natural language into a formal meaning representation. In order to apply such methods to learning from observation, we have developed methods that estimate the meaning of sentences from just their ambiguous perceptual context.